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Separable Differential Equation


A separable differential equation is a first-order ordinary differential equation that can be written

 y^'=g(x)h(y).

On an interval where h(y)!=0, separation of variables gives

 int(dy)/(h(y))=intg(x)dx+C.

Solutions for which h(y)=0 must be checked separately because division by h(y) can remove constant solutions.


See also

Ordinary Differential Equation, Separation of Variables

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References

Boyce, W. E. and DiPrima, R. C. Elementary Differential Equations and Boundary Value Problems, 9th ed. Hoboken, NJ: Wiley, 2009.

Cite this as:

Weisstein, Eric W. "Separable Differential Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SeparableDifferentialEquation.html

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